Complex dynamical behaviours in two non-linearly coupled Chua’s circuits

Abstract

The complex behaviour in the dynamics of a sixth-order circuit oscillator is presented. The oscillator is made up of two smooth Chua’s circuits, which have been properly bi-directionally and non-linearly coupled. The coupled system exhibits synchronization, antisynchronization, hyperchaos and on–off intermittency. The occurrence of hyperchaotic oscillations is marked by the loss of transverse stability of a chaotic attractor belonging to an invariant subspace. The transverse stability condition of such an attractor has been numerically analyzed by referring to both the properties of the flow transverse to the attractor and its linearization. The presence of a blowout bifurcation is confirmed by the calculus of Lyapunov exponents and by the presence of on–off intermittency. Moreover the occurrence of antisynchronization under the hypothesis of weak coupling and of synchronization under the hypothesis of tight coupling are analytically demonstrated and numerically verified through Lyapunov exponents.